Der Casimir-Effekt in der Kugel-Kugel-Geometrie: Theorie und Anwendung auf das Experiment

Die Fertigung von mikroskopischen elektromechanischen Systemen, sog. MEMS, ist in Bereiche vorgedrungen, in denen die ordnungsgemäße Funktion der Maschinen nicht mehr allein auf Basis von Aussagen der klassischen Physik gewährleistet werden kann. Für derartige Maschinen muss u. a. der Casimir-Effekt berücksichtigt werden, welcher besagt, dass Fluktuationen des elektromagnetischen Felds merkliche Kräfte zwischen ungeladenen Objekten verursachen können. In dieser Arbeit wird die Casimir-Wechselwirkung zweier Kugeln aus beliebigen Materialien bei endlichen Temperaturen studiert. Es werden die Ursachen negativer Casimir-Entropie diskutiert und Kraftvorhersagen für ein Experiment vorgestellt, welches zur Messung der Casimir-Kraft erstmals die Kugel-Kugel-Geometrie benutzt

Disentangling geometric and dissipative origins of negative Casimir entropies

Dissipative electromagnetic response and scattering geometry are potential sources for the appearance of a negative Casimir entropy. We show that the dissipative contribution familiar from the plane-plane geometry appears also in the plane-sphere and the sphere-sphere geometries and adds to the negative Casimir entropy known to exist in these geometries even for perfectly reflecting objects. Taking the sphere-sphere geometry as an example, we carry out a scattering-channel analysis, which allows us to distinguish between the contributions of different polarizations. We demonstrate that dissipation and geometry share a common feature making possible negative values of the Casimir entropy. In both cases there exists a scattering channel whose contribution to the Casimir free energy vanishes in the high-temperature limit. While the mode-mixing channel is associated with the geometric origin, the transverse electric channel is associated with the dissipative origin of the negative Casimir entropy. By going beyond the Rayleigh limit, we find even for large distances that negative Casimir entropies can occur also for Drude-type metals provided the dissipation strength is sufficiently small

Geometric origin of negative Casimir entropies: A scattering-channel analysis

Negative values of the Casimir entropy occur quite frequently at low temperatures in arrangements of metallic objects. The physical reason lies either in the dissipative nature of the metals as is the case for the plane-plane geometry or in the geometric form of the objects involved. Examples for the latter are the sphere-plane and the sphere-sphere geometry, where negative Casimir entropies can occur already for perfect metal objects. After appropriately scaling out the size of the objects, negative Casimir entropies of geometric origin are particularly pronounced in the limit of large distances between the objects. We analyze this limit in terms of the different scattering channels and demonstrate how the negativity of the Casimir entropy is related to the polarization mixing arising in the scattering process. If all involved objects have a finite zero-frequency conductivity, the channels involving transverse electric modes are suppressed and the Casimir entropy within the large-distance limit is found to be positive